{"id":3663,"date":"2026-03-21T05:26:56","date_gmt":"2026-03-21T05:26:56","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3663"},"modified":"2026-04-13T07:49:49","modified_gmt":"2026-04-13T07:49:49","slug":"the-lunar-nodes-rahu-and-ketu","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/astronomy\/the-lunar-nodes-rahu-and-ketu\/","title":{"rendered":"The Lunar Nodes (Rahu and Ketu) \u2013 The Mathematics of an Eclipse"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_e1e3db6af71809d1-734\" data-path-to-node=\"29\"><span data-path-to-node=\"29,0\"><b data-path-to-node=\"29,0\" data-index-in-node=\"0\">The Concept<\/b> <\/span><span data-path-to-node=\"29,2\"><span class=\"citation-3327\">Rahu and Ketu are not evil demons but rather the ascending and descending nodes<\/span><\/span><span data-path-to-node=\"29,4\">. <\/span><span data-path-to-node=\"29,6\"><span class=\"citation-3326\">These are the mathematical points at which the Moon&#8217;s tilted orbit intersects the Earth&#8217;s path (the Ecliptic)<\/span><\/span><span data-path-to-node=\"29,8\">. <\/span><span data-path-to-node=\"29,10\"><span class=\"citation-3325\">A lunar eclipse requires the Moon to be close to these nodes<\/span><\/span><span data-path-to-node=\"29,12\">. <\/span><span data-path-to-node=\"29,14\"><span class=\"citation-3324\">The <\/span><i data-path-to-node=\"29,14\" data-index-in-node=\"4\"><span class=\"citation-3324\">Surya Siddhanta<\/span><\/i><span class=\"citation-3324\"> calculates their retrograde motion to the minute, allowing it to predict precisely when and how much of the Sun or Moon will be covered<\/span><\/span><span data-path-to-node=\"29,16\">.<\/span><\/p>\n<p id=\"p-rc_e1e3db6af71809d1-735\" data-path-to-node=\"30\"><span data-path-to-node=\"30,0\"><b data-path-to-node=\"30,0\" data-index-in-node=\"0\">The Story<\/b> <\/span><span data-path-to-node=\"30,2\"><span class=\"citation-3323\">To the ancient world, eclipses were terrifying moments where a celestial dragon swallowed the Sun<\/span><\/span><span data-path-to-node=\"30,4\">. <\/span><span data-path-to-node=\"30,6\"><span class=\"citation-3322\">But Indian astronomers saw past the myth to the math<\/span><\/span><span data-path-to-node=\"30,8\">. <\/span><span data-path-to-node=\"30,10\"><span class=\"citation-3321\">They realized that Rahu and Ketu weren&#8217;t monsters, but invisible &#8220;nodes&#8221;\u2014mathematical points where the Moon&#8217;s tilted path crosses the Earth&#8217;s orbit<\/span><\/span><span data-path-to-node=\"30,12\">. <\/span><span data-path-to-node=\"30,14\"><span class=\"citation-3320\">By creating a 3D model of these intersecting planes, the <\/span><i data-path-to-node=\"30,14\" data-index-in-node=\"57\"><span class=\"citation-3320\">Surya Siddhanta<\/span><\/i><span class=\"citation-3320\"> could predict exactly when and where a shadow would fall<\/span><\/span><span data-path-to-node=\"30,16\">. <\/span><span data-path-to-node=\"30,18\"><span class=\"citation-3319\">This &#8220;Nodal Astronomy&#8221; was so accurate it is still used in traditional Indian <\/span><i data-path-to-node=\"30,18\" data-index-in-node=\"78\"><span class=\"citation-3319\">Panchangs<\/span><\/i><span class=\"citation-3319\"> to this day to track the heartbeat of the sky<\/span><\/span><span data-path-to-node=\"30,20\">.<\/span><\/p>\n<p data-path-to-node=\"31\"><b data-path-to-node=\"31\" data-index-in-node=\"0\">The Timeline<\/b><\/p>\n<table data-path-to-node=\"32\">\n<thead>\n<tr>\n<td><strong>Milestone<\/strong><\/td>\n<td><strong>Details<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"32,1,0,0\"><b data-path-to-node=\"32,1,0,0\" data-index-in-node=\"0\">Western Ref.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_e1e3db6af71809d1-736\" data-path-to-node=\"32,1,1,0\"><span data-path-to-node=\"32,1,1,0,1\"><span class=\"citation-3318\">17th Century CE (Kepler\/Newton)<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"32,2,0,0\"><b data-path-to-node=\"32,2,0,0\" data-index-in-node=\"0\">Indian Source<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_e1e3db6af71809d1-737\" data-path-to-node=\"32,2,1,0\"><span data-path-to-node=\"32,2,1,0,1\"><span class=\"citation-3317\">Prior to 10,000 BCE (<\/span><i data-path-to-node=\"32,2,1,0,1\" data-index-in-node=\"21\"><span class=\"citation-3317\">Surya Siddhanta<\/span><\/i><span class=\"citation-3317\">) <\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"32,3,0,0\"><b data-path-to-node=\"32,3,0,0\" data-index-in-node=\"0\">Chron. Gap<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_e1e3db6af71809d1-738\" data-path-to-node=\"32,3,1,0\"><span data-path-to-node=\"32,3,1,0,1\"><span class=\"citation-3316\">Over 11,000 Years<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"33\"><b data-path-to-node=\"33\" data-index-in-node=\"0\">The Original Text<\/b><\/p>\n<blockquote data-path-to-node=\"34\">\n<p id=\"p-rc_e1e3db6af71809d1-739\" data-path-to-node=\"34,0\"><span data-path-to-node=\"34,0,0\"><b data-path-to-node=\"34,0,0\" data-index-in-node=\"0\">Sanskrit Shloka:<\/b> \u0935\u0915\u094d\u0930\u093e\u0928\u0941\u0935\u0915\u094d\u0930\u0917\u092e\u0928\u093e\u0928\u094d \u092e\u0923\u094d\u0921\u0932\u093e\u0928\u094d\u0924\u0917\u094c \u0927\u094d\u0930\u0941\u0935\u094c \u0964 <\/span><span data-path-to-node=\"34,0,2\"><span class=\"citation-3315\">\u0915\u094d\u0937\u0947\u092a\u0938\u094d\u0924\u0947\u092d\u094d\u092f\u094b\u093d\u092a\u092e\u0923\u094d\u0921\u0932\u0947 \u0938\u093f\u0926\u094d\u0927\u092f\u0924\u094d\u092f\u0930\u094d\u0915\u0917\u094d\u0930\u0939\u093e\u0917\u094d\u0930\u0924\u0903 \u0965 <\/span><\/span><\/p>\n<p data-path-to-node=\"34,0\"><span data-path-to-node=\"34,0,4\"> <b data-path-to-node=\"34,0,4\" data-index-in-node=\"1\">Transliteration:<\/b> Vakr\u0101nuvakragaman\u0101n ma\u1e47\u1e0dal\u0101ntagau dhruvau | K\u1e63epastebhyo&#8217;pama\u1e47\u1e0dale siddhyatyarkagrah\u0101grata\u1e25 || <\/span><span data-path-to-node=\"34,0,6\"><span class=\"citation-3314\">Surya Siddhanta (2.6) <\/span><\/span><\/p>\n<p data-path-to-node=\"34,0\"><span data-path-to-node=\"34,0,6\"><span class=\"citation-3314\">M<\/span><\/span><span data-path-to-node=\"34,0,9\"><b data-path-to-node=\"34,0,9\" data-index-in-node=\"0\"><span class=\"citation-3313\">eaning:<\/span><\/b><span class=\"citation-3313\"> &#8220;From the retrograde and somewhat retrograde motion, the nodes (Dhruva points) move to the end of the circle. Their latitude (deviation) in the ecliptic is established from the position of the Sun and planets.&#8221; <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_e1e3db6af71809d1-740\" data-path-to-node=\"35\"><span data-path-to-node=\"35,0\"><b data-path-to-node=\"35,0\" data-index-in-node=\"0\">Related Innovations<\/b> <\/span><span data-path-to-node=\"35,2\"><span class=\"citation-3312\">Eclipse Colour: Using the depth of the shadow to predict whether the Moon will be red or black<\/span><\/span><span data-path-to-node=\"35,4\">. <\/span><span data-path-to-node=\"35,6\"><span class=\"citation-3311\">Source: <\/span><i data-path-to-node=\"35,6\" data-index-in-node=\"8\"><span class=\"citation-3311\">Surya Siddhanta<\/span><\/i><\/span><span data-path-to-node=\"35,8\">.<\/span><\/p>\n<p id=\"p-rc_e1e3db6af71809d1-741\" data-path-to-node=\"36\"><span data-path-to-node=\"36,0\"><b data-path-to-node=\"36,0\" data-index-in-node=\"0\">Fun Fact<\/b> <\/span><span data-path-to-node=\"36,2\"><span class=\"citation-3310\">The Western astronomical symbols for the North (Omega) and South (mho) Nodes are derived from the Indian Dragon Head (Rahu) and Tail (Ketu)<\/span><\/span><span data-path-to-node=\"36,4\">.<\/span><\/p>\n<p id=\"p-rc_e1e3db6af71809d1-742\" data-path-to-node=\"37\"><span data-path-to-node=\"37,0\"><b data-path-to-node=\"37,0\" data-index-in-node=\"0\">The Modern Legacy<\/b> <\/span><span data-path-to-node=\"37,2\"><span class=\"citation-3309\">Orbital mechanics is the foundation of modern science<\/span><\/span><span data-path-to-node=\"37,4\">. <\/span><span data-path-to-node=\"37,6\"><span class=\"citation-3308\">It is required for determining satellite routes and crossing of orbital planes<\/span><\/span><span data-path-to-node=\"37,8\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3519,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[75],"tags":[84,97,99,100,491,98,85],"class_list":["post-3663","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-astronomy","tag-astronomy","tag-lunar-eclipses","tag-orbital-mechanics","tag-panchang","tag-positional-astronomy","tag-rahu-and-ketu","tag-surya-siddhanta"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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